What are the solutions to the equation x^5-x^4-x+1=0 ?

The solutions to the equation x^5-x^4-x+1=0 are x=1,x=i,x=-i,x=-1

Find the zeros of x^5-x^4-x+1=0

The zeros of x^5-x^4-x+1=0 are x=1,x=i,x=-i,x=-1

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x^{5} - x^{4} - x + 1 = 0

x = 1, x = i, x = - i, x = - 1

Solution steps

x^{5} - x^{4} - x + 1 = 0

Factor

x^{5} - x^{4} - x + 1 : (x - 1)^{2} (x^{2} + 1) (x + 1)

(x - 1)^{2} (x^{2} + 1) (x + 1) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 1 = 0 or x^{2} + 1 = 0 or x + 1 = 0

Solve

x - 1 = 0 : x = 1

Solve

x^{2} + 1 = 0 : x = i, x = - i

Solve

x + 1 = 0 : x = - 1

The solutions are

x = 1, x = i, x = - i, x = - 1

2 x^{3} + 5 x - 3 = 0

2 x^{4} - 50 x^{2} = 0

2 x^{3} - x^{2} - 18 x + 9 = 0

- x^{3} + 5 x^{2} - 8 x + 4 = 0

x^{4} = 625

What are the solutions to the equation x^5-x^4-x+1=0 ?
The solutions to the equation x^5-x^4-x+1=0 are x=1,x=i,x=-i,x=-1
Find the zeros of x^5-x^4-x+1=0
The zeros of x^5-x^4-x+1=0 are x=1,x=i,x=-i,x=-1